Exams › SSC CGL (Prelims) › General

An observer on a cliff 200 m high notices the angles of depression to two ships located on opposite sides as 60° and 30°. Find the distance between the two ships.

1. 400 \(\sqrt{3}\) m
2. 200 \(\sqrt{3}\) m
3. 800 \(\sqrt{3}/3\) m
4. 200 \((\sqrt{3} + 1)\) m

Correct answer: 800 \(\sqrt{3}/3\) m

Solution

For an angle of depression, the horizontal distance from the cliff base is found using \(\tan\theta = \frac{\text{height}}{\text{distance}}\). Thus the distances are \(200/\tan 60^\circ = 200/\sqrt{3}\) and \(200/\tan 30^\circ = 200\sqrt{3}\). Since the ships are on opposite sides, the total distance is their sum, which simplifies to \(800\sqrt{3}/3\) m.

Related SSC CGL (Prelims) General questions

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• Given that angles \(A\) and \(B\) are complementary and \(\cos A=\frac{5}{13}\), what is \(\tan B\)?
• What is the radian measure of $135^\circ$?
• If $\sin^2\theta-\cos^2\theta=-\frac{1}{3}$, find the value of $\cos^2\theta$.
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